the two legs have lengths of x-6 feet and x+9 feet. The hypotenuse is 2x-27 feet. Find the lengths of the three sides

Question

(x-6)^2+(x+9)^2=(2x-27)^2

Answer 1

Sum of the squares of the two legs is 2x²+6x+117=4x²-108x+729 (hypotenuse squared)

2x²-114x+612=0

x²-57x+306=0=(x-6)(x-51)

Therefore x=6 or 51. We can reject x=6 because x-6 is the length of a leg. So x=51.

The sides are 45, 60 and 65 (Pythagorean 5-12-13 triangle).